Fundamentals of Physics Extended (10th Edition)

by
Halliday, David; Resnick, Robert; Walker, Jearl

Published by
Wiley

ISBN 10:
1-11823-072-8

ISBN 13:
978-1-11823-072-5

Chapter 2 - Motion Along a Straight Line - Problems: 107

Answer

$\Delta t=0.57s$

Work Step by Step

All units must be in SI units. For speed, it is meters per second. Performing dimensional analysis on $v=100km/h$ yields a speed of a $$=\frac{100km}{1hr} \times \frac{1hr}{60min} \times \frac{1min}{60s} \times \frac{1000m}{1km}$$ $$=27.8m/s$$ Use the formula for acceleration $$a=\frac{\Delta v}{\Delta t}$$ to solve for $\Delta t$. $$\Delta t=\frac{\Delta v}{a}$$ Substitute known values of $v=27.8m/s$ and $a=50m/s^2$ yields a change in time of $$\Delta t = \frac{27.8m/s}{50m/s^2}=0.57s$$